I've been playing guitar for a while now but I've always played rhythm and never really ventured very far into lead guitar so I've decided to practice a few solos this summer to make myself a more accomplished guitarist.

Now, In "I believe in a thing called love" by The Darkness I'm having trouble with the second solo and this kinda technique has come up in a few things I've tried to learn. I think it would be a great help if I could learn how to easily do these kinda things.
at 2:22 it is

This part:


What are some daily practices I can do and gradually build up the speed of it that will get me doing this kinda thing?

Well playing that never hurt. You want to practice to play that by practicing other stuff?
Just use a metronome nice and slow like 60% speed and get it perfect. Play it perfect 20 times then add speed. Rinse, repeat.
Yeah, I just thought there might be something I could practice to make it easier to play this kinda stuff. I thought just practicing that part alone might make it hard to apply it to other solo's and stuff.

So you'd literally just rinse this little part until it becomes fluent?
I for one would first of all instead of the 15 and 14 fret on the D string would play the 10th and 9th fret on the G string (exactly the same note, just in an easier to reach spot)
as for the rest, take it slow and practice
i practice hammer ons and pull offs by playing scales to a metronome